Yes, it is all a great mystery. Was wondering when I read the earlier post about this bit about the baptismal certificate "Under the Names of Parents are her father's name, and the name of a woman Laura doesn't know (and never has). The woman that brought her up as, and Laura always thought was her 'mum' never showed her love or affection of any kind which has made her feel that perhaps she might not have been - the fact that her name doesn't appear on the baptism certificate has obviously raised a million questions which no one can answer - every one's dead."
If her father is listed on the baptismal cert. then it sounds like he would have been her father, so, could he have originally been married to the woman on the cert. when Laura was born, mother died/parents divorced/unable to care for Laura/children so they were placed in care for a little while. Then, when he met/married another woman Laura was taken back from care and raised by them.
If father & 2nd wife when to court to adopt her then a new certificate might have been ordered in 1976.
Another point is that although the 'parents' are named on the 1961 bapt. cert. it doesn't necessarily mean that both were present at the baptism. Are there any godparents listed?